Nuclear structures: Twinning and modulation in crystals

Crystal structure analysis is a standard technique routinely applied to single crystals as well as powders. However the process is not so straightforward if the crystal sample is affected by twinning or if the structure is modulated. In such cases the standard procedures are not directly applicable. The main purpose of this contribution is to show how to solve and refine such difficult structures. While for twinned structures the basic property of crystal – translation symmetry in three dimensional space–remains valid, for modulated crystals a special superspace theory must be exploited in order to describe the atomic structure with crystallographic methods generalized for superspace